12 required, thus : Divide it by 3; divide the result by 10, and then the result of this divi- 3)260730£ sion by 10, in each case disregarding re- 86910 mainders. Add up the four numbers, as in the 8691 margin, and point off five places for decimals. 869 The result is 1.00009, which differs from unity by a quantity too insignificant to de- 3:57200£ serve notice. These operations, therefore, per 20 formed upon the dividend, will give the interest with all necessary accuracy. Let us, 11.440 8. for instance, apply them to the dividend 260730 above, disregarding the 108., since the 73000th part of it is of no moment. You 5.28 d. see that the result is £3 118. 5 d., as before ; 4 and that it differs from the strictly accurate conclusion above only by a fraction of a far- 1.12 f. thing. It is this method which I would recom- £956.725 mend you always to adopt in computing interest for days. I here give another example of it, which, 6697.075 for variety, is worked in the margin by de 9 cimals. 2. What is the interest of £956 148. 6d. 60273.675 for 7 days, at 41 per cent. ? 3) 60274 Here, 148. 6d. is reduced to the decimal of 20091 a £, and the product by the days multiplied 2009 by double the rate: the decimal of a £, in 200 the resulting product, is rejected, and the integral value increased by unit. The answer 82574€ is £0 168. 6d. 20 NOTE. When the interest is 5 per cent., then, since the double of the rate is 10, we 16:5148 8. have only to multiply by the number of days, 12 and to point off but four places from the result of the remaining operations. 6.1776 d. (108.) You perceive that the particulars concerned in interest-calculations are these four, namely, Principal, Rate, Time, and Interest; the Amount is merely the sum of two of these, the principal and the interest. In the preceding examples, the three of these which have been given to find the fourth are the first three; but any other three being given, the fourth may be found, simply by reversing one or more of the operations exhibited above. Ex. 1. In what time will £91 13s. 4d. amount to £105 6s. Old. at 44 per cent. ? The principal and amount being given, the interest is given, namely, £13 128. 8£d.; and we want to know the number of years which has produced this amount of interest. For this purpose it is clearly only necessary to divide £13 128. 84d. by 1 year's interest. d. d. 91 13 4 13 12 82 4. 20 £. S. £. s. 1870, halfpence. 2. What principal put out to interest for 3 years, at 44 per cent., will amount to £105 68. ? For a principal of £100, the amount in the given time at the given rate is £100+£4.25 x 3.5 = £114.875. Consequently, since £105 68.= £105-3 114.875 : 105.3 :: £100 : £91 13s. 4d. Ans. £. £. 1,1,487,5/10530 (91.667 103388 20 3. What must be the rate per cent. in order that £142 10s. may amount to £163 138. 11d. in 44 years ? Here the interest is £21 3s. 11d., which is what would arise from multiplying £142 10s. by 41, by the rate, and dividing by 100: consequently, we have only to divide £142 108. by 100, to multiply the quotient by 41, and then to divide £21 38. 11d. by the result, in order to get the rate. There can be no sensible 142 10 error in the rate by making 20 the amount £163 14s. in £. 8. d. stead of £163 138. 11d.; in 2850 21 3 11 which case the interest is 12 20 £21 4s. = £21.2: we may therefore work thus by de342,00 423 4. 12 £1.425=principal: 100 41 1368 5087 852 2 5.700 •35625 1453£ X 2=2907)10174(3), rate. £. 8721 £6,-0.5625.)21-2(3-5, rate. 182 .30 cimals : In the second method here given, all those decimals of the divisor have been cut off which, upon multiplication by the quotient-figure, would fall to the right of the decimal 2 in the dividend, agreeably to what has been taught in contracted division, because the decimal •2 is not strictly accurate, although the error is very minute. Exercises. 1. What is the interest of £9826 138. 8d. for 1 year, at 2 per cent. ? 2. What is the interest of £896, for 2} years, at 34 per cent. ? 3. What is the interest of £98 198. 6d. for 11 months, at 3 per cent. ? 4. What is the interest of £3204 14s. for 37 days, at 5 per cent. ? 5. What is the interest of £256, from May 7 till Aug. 12, at 4į per cent. ? 6. What is the interest of £319 Os. 6d. for 5 years, at 3 per cent. ? 7. What is the amount of £120, from Jan. 7 to Sept. 12, 1852 (leap year), at 4 per cent. ? 8. What principal will produce a yearly interest of £341 58. at 5 per cent. ? 9. In what time will £2000 amount to £2280, if lent at 3 per cent. ? 10. If £42 38. 9d. be received for interest on £11250 for 1 month, what is the rate per cent. per annum? 11. What is the interest of £193 12s. at £11 18s. 6d. per cent. ? 12. The amount of money expended for the maintenance of the poor by the 607 unions of England and Wales, during the year ending at Michaelmas 1850, was £3469857, and during the year ending at Michaelmas 1851 the amount was £3288192; what was the de crease per cent. ? 13. The population of Great Britain in 1841 was 18664761, and in 1851 it was 20936468: required the increase per cent. during the intervening ten years. 14. The population of Ireland in 1841 was 8175124, and in 1851, 6515794: required the decrease per cent. (109.) Discount, in the usual meaning of the term, is only another name for Interest. In commercial transactions, payments are not always made in money, but often in what are called Bills of Exchange or Promissory Notes. These are stamped slips of paper, on which engagement is made to pay in cash, after the lapse of a specified time. The present worth of such a Bill, is that sum of money, paid down, which, when put out at the proposed interest for the specified time, will amount to just sufficient to pay the Bill when it becomes due. Thus, if the Bill be for £105, payable in one year, interest being at 5 per cent., then, since £100 present money would amount in one year to £105, if placed out at the proposed interest, £100 is the present worth of the Bill; the £5 thus allowed for cashing it being the true deduction or Discount. But Bankers do not discount Bills on these terms: it is not reasonable to expect they should: they must make a profit by this as well as by other departments of their business, and, therefore, they would charge, as discount, the full interest of the £105 for one year, namely, £5 58. ; so that by discount, commercial men understand interest upon the sum discounted, during the period for which the payment of that sum is delayed; what remains, after the deduction of this discount, is all that is paid down for a Bill, as its present worth ; hence, to calculate the discount of a sum of money, is the same as to calculate the interest of that sum, the time and rate per cent. being given. In Bills, however, three days, called days of grace, are added to the time specified for payment:* thus, if a Bill be drawn for three months after date, and be dated on the 1st of January, it does not become due till the 4th of April; and the interest or discount is accordingly calculated for three months and three days. In general, the whole time the Bill has to run is turned into days, and the interest computed as at page 160. The following Table will be found very convenient in calculations of this kind. Table for the Number of Days from any Day in one Month to the same Day in another. Remember that in Leap Year another day is to be added to February. Jan. Feb. Mar. Apr. May June July Aug. Sep. Oct. Nov. Dec. January 365 31 59 90 120 151 181 212 243 273 304 334 February 334 365 28 59 89 120 150 181 212 242 273 303 March 306 337 365 31 61 92 122 153 184 214 245 275 April 275 306 334 365 30 61 91 122 153 | 183 214 244 May.. 245 276 304 335 365 31 61 92 123 153 184 214 June.... 214 245 273 304 334 365 30 61 92 122 153 183 July 184 215 243 274 304 335 365 31 62 92 123 153 August. . 153 184 212 243 273 304 334 365 31 61 92 122 Septemb. 122 153 181 212 242 273 303 334 365 30 61 91 October../ 92 123 151 182 212 243 273 304 335 365 31 61 Novemb. 61 92 120 151 181 212 242 273 304 334 365 30 Decemb. 31 62 90 121 151 182 212 243 274 304 335 365 The reason of this is, that the law allows the indulgence of three days to the acceptor of a bill, as the person on wbom it is drawn is called, before legal proceedings can be issued against him for non-payment; but the bankers take care that the “indulgence" shall be paid for. The acceptor becomes legally responsible for the payment of the bill by simply writing his name across it, by doing which he is said to accept it. |